Three points P, Q, and R lie on the line segm | vedclass

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(D) The points $P, Q,$ and $R$ divide the line segment $AB$ into four equal parts. Thus,the ratio $AR:RB$ is $3:1$.Using the section formula,if a poin

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$(9/2, -5/2)$

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(D) The points $P, Q,$ and $R$ divide the line segment $AB$ into four equal parts. Thus,the ratio $AR:RB$ is $3:1$.Using the section formula,if a point $(x, y)$ divides the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ in the ratio $m:n$,the coordinates are given by:$x = \frac{mx_2 + nx_1}{m+n}, y = \frac{my_2 + ny_1}{m+n}$For point $R$,$m=3$ and $n=1$,with $A(-6, 8)$ and $B(8, -6)$:$x = \frac{3(8) + 1(-6)}{3+1} = \frac{24 - 6}{4} = \frac{18}{4} = \frac{9}{2}$$y = \frac{3(-6) + 1(8)}{3+1} = \frac{-18 + 8}{4} = \frac{-10}{4} = -\frac{5}{2}$Therefore,the coordinates of $R$ are $(\frac{9}{2}, -\frac{5}{2})$.

Three points $P, Q,$ and $R$ lie on the line segment joining points $A(-6, 8)$ and $B(8, -6)$ such that $AP = PQ = QR = RB$. Find the coordinates of $R$.

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